The arrangement of electrons within an atom dictates its chemical behavior and its place in the periodic table. Electrons occupy specific regions of space called atomic orbitals, which are defined by the complex mathematical rules of quantum mechanics. These rules describe the probability of finding an electron in a particular location. This framework allows scientists to determine the precise capacity of these electron housing areas, including the ‘f’ orbital, which is important in the structure of many heavy elements.
Defining the Subshell Structure
The organization of electrons begins with electron shells, designated by the principal quantum number (\(n\)), which describes the electron’s energy level. Within each shell, electrons are grouped into subshells, denoted by letters: s, p, d, and f. The subshell defines the general shape of the region where the electron is likely to be found. For instance, the ‘s’ subshell contains one orbital, while the ‘p’ subshell contains three. The ‘f’ subshell represents a group of orbitals with complex, multi-lobed spatial shapes.
The Maximum Electron Capacity
The maximum number of electrons that can be held within the entire ‘f’ subshell is fourteen. The total capacity of a subshell is determined by the number of individual orbitals it contains, multiplied by the maximum number of electrons each orbital can hold. The rule governing electron filling is the Pauli Exclusion Principle, which states that no two electrons in an atom can share the exact same set of quantum properties. This principle restricts the occupancy of any single atomic orbital to a maximum of two electrons. For two electrons to occupy the same orbital, they must possess opposite magnetic spin states.
Deriving the F Orbital Orientations
The number of individual orbitals within the ‘f’ subshell is determined by the angular momentum quantum number (\(l\)), where ‘f’ corresponds to an \(l\) value of \(3\). The number of unique orientations is calculated using the magnetic quantum number (\(m_l\)), which can take any integer value from \(-l\) through zero to \(+l\). For the ‘f’ subshell where \(l=3\), the possible values for \(m_l\) are \(-3\), \(-2\), \(-1\), \(0\), \(+1\), \(+2\), and \(+3\). This calculation results in seven distinct values, meaning there are seven unique ‘f’ orbitals that exist within the subshell. Since each orbital can accommodate a maximum of two electrons, the total electron capacity is fourteen electrons (seven orbitals multiplied by two electrons), which is why the ‘f-block’ on the periodic table contains elements that are fourteen spaces wide.
Placement of F Orbitals in the Elements
The filling of the ‘f’ subshell begins in the sixth and seventh periods of the periodic table. Elements actively filling their ‘f’ orbitals make up the two rows placed beneath the main body of the table, known as the f-block elements. These elements are called the inner transition metals because the electrons fill an inner shell rather than the outermost shell. The two series within the f-block are the Lanthanides, which fill the \(4f\) orbitals, and the Actinides, which fill the \(5f\) orbitals. The Lanthanides are found in the sixth period, while the Actinides are located in the seventh period.